Supporting segments featured the Bungle Brothers, a canine duo who sought vaudeville stardom; Crazy Claws, a witty wildcat who lived in a national park and was hunted by the fur trapper Rawhide Clyde, and Dirty Dawg, a canine vagrant who, with his rodent sidekick Ratso, sought "the pot of stew at the end of the rainbow".
This series provides examples of:
- Accessory-Wearing Cartoon Animal: Kwicky only wears neck wear.
- Ageless Birthday Episode: "Around the World in 80 Seconds" is one with Wilford Wolf celebrating his own birthday trying to catch Kwicky for himself.
- Alliterative Name: Kwicky Koala and Wilford Wolf.
- Awkward Father-Son Bonding Activity: This principle is in effect except it's Uncle and Nephew in "Double Trouble". Ruffy wants to be friends with Kwicky, while Wilford wants to teach him to hunt him.
- Batman Can Breathe in Space: At the End of "Kwicky's Karnival Kaper" Wilford sits up in space on a small piece of space rock and tries to bum a ride from a ufo with no need of oxygen.
- Flash Step: How Kwicky often escapes from danger, accompanied by a beep sound effect.
- Fractured Fairy Tale: "In A Pig's Eye" is a very loose example. Wilford wants to eat the three little pigs but Kwicky lives in their house now. But they do show up at the very end.
- Funny Animal: Kwicky and Wilford are both ones.
- High Koala-ty Cuteness The titular marsupial is depicted as innocent, albeit using his surprising speed (setting him from other Koalas) to escape Wilfred Wolf.
- Laid-Back Koala: Kwicky is an inversion as he lives up to his name, being able to move at Flash Step speeds to escape the pursuing Wilford Wolf.
- Obfuscating Stupidity/Unknown Rival: Kwicky often goes through Wilford's traps, seemingly having no idea that he was in a trap in the first place... except for those moments where he [Kwicky] seems to know but acts like he doesn't to make it easier to trick Wilford. The ambiguity is never resolved.
- Species Surname: Both Kwicky Koala and Wilford Wolf.
- Tangled Family Tree: Wilford Wolf meets his nephew Ruffy Wolf.
- Three Shorts: Kwicky Koala was the A, Crazy Claws the B and Dirty Dawg was the C. Bungle Brothers bumpers ran before each.
- Trademark Favorite Food: Kwicky and his eucalyptus leaves.
- Unexpected Inheritance: In "Race to Riches", Kwicky receives one from his now deceased Uncle Jeremiah Koala.